A three-dimensional force balance model for predicting bubble departure in conventional circular tubes

Context. Mass loss in oxygen-rich asymptotic giant branch (AGB) stars remains a longstanding puzzle, as the dust species detected around these stars appear too transparent to drive winds through the absorption of radiation alone. The current paradigm consists of outflows driven by photon scattering and requires relatively large grains (∼0.3 μm). Whether the necessary number of grains with the required scattering properties exist around AGB stars remains to be determined empirically. Aims. We test whether the dust grains observed around the oxygen-rich AGB star R Doradus can drive its stellar wind by combining, for the first time, polarimetric constraints with elemental abundance limits and force balance calculations. We examine Fe-free silicates (MgSiO 3 ), aluminium oxide (Al 2 O 3 ), and Fe-bearing silicates (MgFeSiO 4 ) to determine whether any dust species can generate sufficient radiative pressure under physically realistic conditions. Methods. We analysed high-angular-resolution polarimetric observations obtained with SPHERE/ZIMPOL at the Very Large Telescope (VLT) and modelled the circumstellar dust using the radiative transfer code RADMC-3D. Dust optical properties were computed using Optool for both Mie and the distribution of hollow spheres (DHS) scattering theories. By systematically exploring a six-dimensional parameter space, we derived constraints on dust grain sizes, density profiles, and wavelength-dependent stellar radii. For models that successfully fit the observations, we analysed the results taking into consideration recent models for the gas density distribution around R Dor, and applied a multi-criteria zone analysis incorporating gas-depletion constraints and radiation pressure thresholds to assess dust-driven wind viability. Results. We find sub-micron MgSiO 3 and Al 2 O 3 grains (up to 0.1 μm) regardless of scattering theory considered, and a two-layer dust envelope with steep density profiles (r −3.4 to r −4.1 ). Despite matching observed scattered-light patterns, these grains generate insufficient radiative force under physically realistic gas-to-dust mass ratios, even when assuming complete elemental depletion. Silicates containing Fe could theoretically provide adequate force, but would sublimate in critical acceleration regions and require implausibly high silicon-depletion levels. Conclusions. Our findings for R Doradus show insufficient radiation pressure from scattering on grains, suggesting that dust alone cannot drive the wind in this star and that additional mechanisms may be required.

Abstract South Asia has been embroiled in an action-reaction arms race dynamic for over half a century, marked by several episodes of crises and conflict between India and Pakistan. Following overt nuclearisation in 1998, both countries have continued to develop their conventional and nuclear forces, while India has pursued space for limited war through progressive doctrinal and capability enhancements. Pakistan has responded proportionately through doctrinal evolution and force modernisation to close perceived gaps in its deterrence posture. However, since the 2020 India-China Ladakh crisis, India’s conventional superiority with Pakistan has eroded, prompting greater reliance on its dual-use missile arsenal and latent nuclear potential.

Abstract The human eye, a mechanically dynamic and physiologically vital organ, sustains continuous mechanical activity through repetitive blinking—averaging approximately 20000 cycles daily, while exhibiting exceptional lubrication performance characterized by an ultralow coefficient of friction (COF < 0.01). This remarkable lubricating functionality is mediated by the tear film, a multifunctional biological lubricant combining boundary lubrication mechanisms (via adsorbed mucins and lipids) and fluid film lubrication mechanisms to minimize friction and wear, and preserve ocular surface integrity. Failure of such ocular lubrication can cause tear film instability or ocular surface damage, leading to discomfort, visual dysfunction, and dry eye syndrome. Ocular lubrication involves multiple structures and lubricants with highly complex biomolecular interactions. Insights into the structure of eyes, lubricant composition, and causes of functional impairments are essential for addressing friction-related diseases in biological systems. This review examines ocular lubrication by first exploring the biological structure of eyes and typical lubrication modes. Then, the characterization tools, such as tribometer, atomic force microscope, and surface force balance in the field of ocular lubrication, are introduced, followed by a comparison of their working principles, applicable conditions, and application fields. Finally, the specific causes of dry eye syndrome are outlined, along with current bio-lubricants, contact lenses, and other ocular-inspired bio-lubricating materials.

Abstract The present study introduces a novel numerical framework for solving the time fractional Fornberg–Whitham equation (TF-WE) and its modified variant (TMF-WE), which model fluid motion, force balance, and energy transfer in nonlinear wave systems. We construct an innovative operational integration matrix based on orthonormalized Detour polynomials derived from Wheel graphs, a graph-theoretic basis newly applied to fractional partial differential equations. The Caputo fractional derivative is employed to capture memory effects, and the spectral collocation method transforms the governing equations into algebraic systems that are solved via the Newton–Raphson iteration. Five numerical scenarios are explored, demonstrating exponential convergence, reduced memory usage, and superior accuracy compared to existing semi-analytical and numerical methods. The proposed Detour polynomial collocation method (ÐCM) achieves third-order accuracy and efficiently resolves kink-like, peakon, and solitary wave solutions. These results suggest that ÐCM is a scalable and robust tool for modelling complex fractional wave phenomena.

Foams and dense emulsions display complex mechanical behavior, including intermittent rearrangement dynamics, power-law rheology, and slow recovery after perturbation. These effects have long been considered evidence for glassy physics in these and other materials having similar mechanics, such as the cytoskeleton. Here, we study such anomalous mechanics in a simulated wet foam driven by ripening and find behavior that has a different physical origin than that in glasses. Rather, the dynamics is due to a balance of forces from the system's self-similar potential energy landscape and viscous stress. At the lowest viscosities, bubbles move intermittently, with the system shifting abruptly between shallow potential energy minima. For higher viscosities, in contrast, the bubbles move continuously and the system follows a tortuous, fractal path through high-dimensional configuration space, at higher mean energy than the lower viscosity case. The long-time dynamics and power-law rheology are the direct consequence of the potential energy landscape's self-similar geometry. Last, we find that the slow recovery of perturbed foams is due to the foam being kinetically rather than energetically trapped in high-energy portions of the energy landscape. Overall, viscous ripening foams follow a biased energy minimization pathway that explores regions of the energy landscape that are qualitatively different (flatter and smoother) than those corresponding to well-annealed glasses.

Abstract As a typical research object in the interdisciplinary field of electrostatics and fluid mechanics, the solution of the surface tension coefficient of a charged spherical soap bubble under mechanical equilibrium is of great significance for understanding the interface charge distribution, the mechanism of surface tension action, and multi-physics field coupling problems. This paper focuses on a spherical soap bubble with negligible thickness and uniformly charged surface. Under the conditions of given initial radius and electric potential, and equal internal and external air pressure at equilibrium, the expressions of its surface tension coefficient are derived using three different approaches: the force balance analysis method, the potential energy extremum method, and the work-energy relationship method. Through the force balance method, the force analysis of the micro-element on the soap bubble surface is conducted to clarify the balance relationship between electrostatic force and surface tension. By means of the potential energy extremum method, the total potential energy function of the system is constructed, and the solution is obtained by combining the characteristic that the potential energy is minimized at equilibrium. Based on the work-energy relationship method, the result is derived by analyzing the correlation between the work done by electrostatic pressure, the change of potential energy, and the surface tension pressure. All three methods yield consistent expressions for the surface tension coefficient, verifying the reliability of the solution results. Meanwhile, combined with practical application scenarios, such as the stability of charged droplets in electrostatic spray technology and the behavior of charged aerosols in the atmosphere, the practical significance of this research is discussed, providing a theoretical reference for the design and analysis in related engineering fields.

Reliable and accurate particle number concentration measurements are essential across various fields, including clinical diagnostics, environmental monitoring, and industrial applications. Flow cytometry is widely used for these measurements, where the use of counting beads is a common approach. However, this method can introduce size-dependent bias when the target particles differ in size from the counting beads. To evaluate size-dependent bias, this study systematically compares the conventional counting bead-based method with a sample loop-based method that relies on total counting with a defined sample volume. Experimental results show that while both methods yield similar concentrations for beads of comparable size, discrepancies arise when there are significant size differences between the counting beads and target particles. To investigate the cause of this bias, simulations based on force balance analysis were conducted, revealing that larger beads experience stronger forces that facilitate their movement toward the detection area, while smaller beads are more influenced by Brownian motion, which impedes their overall motion. These findings provide a mechanistic explanation for the observed size-dependent bias, confirming that differences in hydrodynamic behavior contribute to variations in bead distribution and motion. By using the sample loop method, which minimizes size-dependent bias, and employing an empirical equation derived from the results, this study offers a reliable approach for predicting and mitigating bias in particle concentration measurements. This work therefore contributes to the development of more precise and traceable methods for particle number concentration measurement, with implications for a wide range of biological and industrial applications.

ABSTRACT In grouting engineering, constant flow and constant pressure modes are widely used, yet existing models struggle to accurately describe grout diffusion, especially with spatiotemporal viscosity variations. To address this, diffusion models for grout under both modes were derived using Newton's fluid mechanics principles and the rheological properties of rapid‐setting slurry. These models were developed through force balance analysis of micro‐elements, mathematical integration, and numerical solutions. The study examines diffusion radius, velocity, and pressure distribution in micro‐fractures, analyzing scenarios with and without viscosity variations. It evaluates the impacts of flow rate, pressure, viscosity, and fracture geometry on diffusion behavior. A three‐dimensional numerical grouting model, employing the two‐phase flow level set method, was developed to simulate the diffusion process, validating the derived models’ reliability. The effects of grouting time, fracture size, flow rate, and pressure on diffusion characteristics were systematically analyzed. A quantitative comparison of constant pressure and constant flow modes was conducted to guide mode selection in grouting engineering. Key findings include: (1) In constant‐flow mode, viscosity changes cause non‐linear pressure decreases as the diffusion radius grows, requiring higher pressures for sustained flow, impacting equipment costs during extended grouting. (2) In constant‐pressure mode, viscosity increases flow resistance, slowing expansion, with radius and velocity stabilizing over time. (3) Constant flow ensures stable diffusion for precise control, while constant pressure enables faster diffusion with significant pressure fluctuations, ideal for rapid filling. This study provides critical insights for optimizing grouting operations and enhancing efficiency in complex geological conditions.

Abstract One of the common tasks required for designing new plasma scenarios or evaluating capabilities of a tokamak is to design the desired equilibria using a Grad-Shafranov (GS) equilibrium solver. However, most standard equilibrium solvers are time-independent and do not include dynamic effects such as plasma current flux consumption, induced vessel currents, or voltage constraints. Another class of tools, plasma equilibrium evolution simulators, do include time-dependent effects. These are generally structured to solve the forward problem of evolving the plasma equilibrium given feedback-controlled voltages. In this work, we introduce GSPulse, a novel algorithm for equilibrium trajectory optimization, that is more akin to a pulse planner than a pulse simulator. GSPulse includes time-dependent effects and solves the inverse problem: given a user-specified set of target equilibrium shapes, as well as limits on the coil currents and voltages, the optimizer returns trajectories of the voltages, currents, and achievable equilibria. This task is useful for scoping performance of a tokamak and exploring the space of achievable pulses. The computed equilibria satisfy both Grad-Shafranov force balance and axisymmetric circuit dynamics. The optimization is performed by restructuring the free-boundary equilibrium evolution (FBEE) equations into a form where it is computationally efficient to optimize the entire dynamic sequence. GSPulse can solve for hundreds of equilibria simultaneously within a few minutes. GSPulse has been validated against NSTX-U and MAST-U experiments and against SPARC feedback control simulations, and is being used to perform scenario design for SPARC. The computed trajectories can be used as feedforward inputs that are connected to the feedback controller to inform and improve feedback performance. The code for GSPulse is available open-source at github.com/jwai-cfs/GSPulse_public

This paper investigates internal structure-driven density changes of post-wildfire and natural debris flows resulting from sand hydrophobicity and shearing. Hydrophobic sand particles entrap air by way of an armoured bubble/gas marble mechanism in water. Although individual armoured bubbles have already been broadly investigated, the effects of fluid drag and collisions in multiphase water–air–sand mixtures remain largely unexplored. The armoured bubbles’ stability in water depends on the force balance on the air bubble–particle boundary, which largely defines the mixture’s internal structure. Gravity, relative armoured bubble and fluid velocities govern the collision forces, local changes in mixture concentration, and the separation or attachment of hydrophobic particles to air bubbles in water. The initially large entrapped air volume decreases due to degassing and large armoured bubble breakdowns downstream. Experimental and theoretical approaches quantify the air entrapment under different sand-water volumetric concentrations, as well as the effects of mixing speed, duration, and sand particle size on the final mixture’s internal structure. Since hydrophobic sand particles can effectively entrap many air bubbles in the final debris flow-like mixture, the densities of debris flows that sweep over hydrophobic soil will accordingly reduce. Therefore, this paper proposes empirical estimates of density reductions resulting from air entrapment.

The article considers the background and activities of the China-Arab Sates Cooperation Forum for two decades. The authors identify key factors and features of the Sino-Arab relations, main priorities of their cooperation, highlight the stages of the Forum activities. They present description of the main models of partnership between the PRC and the Middle East countries. A special attention is paid to the results, problems and prospects of the Forum. The methodological basis of the study is an interdisciplinary approach. The authors adhere to the paradigm of neorealism, particularly the theory of the balance of power and regional security complexes, the principle that posits that the logic of the international system and balance of force among states determine their foreign policy. The «power transit» theory allows to better understand the role of China that has been transforming into a superpower in world politics. The China-Arab States Cooperation Forum activities, despite the existing problems and risks, bring positive results to the participants. It makes a significant contribution to implementation of ambitious plans for «national revival», economic and political prosperity of both the PRC and the Arab countries. The authors come to the conclusion that in the current political realities the parties understand expediency of further cooperation aimed at strengthening bilateral ties. Since Beijing’s relations with Arab partners go beyond purely economic interests and affect the strategic interests of China, which is actively promoting a large-scale Belt and Road initiative. Their close multisectoral cooperation, updated by pragmatic factors, will largely determine the economic prospects and geopolitical significance of both parties in the formation of a multipolar world.

High-sulfur gas fields playing a vital role in oil and gas production. However, sulfur particle deposition can cause equipment corrosion, pipeline blockages, and reduced gas output. Existing critical sulfur-carrying velocity models often neglect particle agglomeration, retention, and wellbore inclination, resulting in large model errors. In this study, a multiphase flow experimental device was used to study the effects of different well inclination, particle flow rate, and gas flow rate on migration and critical sulfur-carrying velocity. Based on force balance, mainly considers the effects of gravity, buoyancy, and friction, while also incorporating parameters such particle aggregation, retention rate, wellbore inclination, and drag force correction coefficient of irregularly shaped particles. A new drag coefficient was obtained by fitting literature data using Levenberg–Marquardt Algorithm and a global optimization algorithm, establish a new critical sulfur-carrying velocity model. Sensitivity analysis shows that critical sulfur-carrying velocity first increases then decreases with wellbore inclination, increases with particle diameter and density, and decreases with higher particle flow rate. Model validation with experimental and field data shows a 3.1% absolute error. This model provides a more accurate theoretical basis for predicting sulfur deposition in high-sulfur gas wells.

We explore the fundamental flow structure of temporally evolving inclined gravity currents with direct numerical simulations. A velocity maximum naturally divides the current into inner and outer shear layers, which are weakly coupled by momentum and buoyancy exchanges on time scales that are much longer than the typical time scale characterising either layer. The outer layer evolves to a self-similar state and can be described by theory developed for a current on a free-slip slope (Van Reeuwijk et al. 2019, J. Fluid Mech., vol. 873, pp. 786–815) when expressed in terms of outer-layer properties. The inner layer evolves to a quasi-steady state and is essentially unstratified for shallow slopes, with flow statistics that are virtually indistinguishable from fully developed open channel flow. We present the classic buoyancy–drag force balance proposed by Ellison & Turner (1959, J. Fluid Mech., vol. 6, pp. 423–448) for each layer, and find that buoyancy forces in the outer layer balance entrainment drag, while buoyancy forces in the inner layer balance wall friction drag. Using scaling laws within each layer and a matching condition at the velocity maximum, the entire flow system can be solved as a function of the slope angle, in good agreement with the simulation data. We further derive an entrainment law from the solution, which exhibits relatively high accuracy across a wide range of Richardson numbers, and provides new insights into the long runout of oceanographic gravity currents on mild slopes.

The structural safety of multi-span ultra-high-voltage (UHV) substation gantries is a cornerstone for the reliability and resilience of sustainable energy grids. The wind-resistant design of the structures is complicated by their complex modal behaviors and highly non-uniform wind load distributions. This study proposes a novel hybrid framework that integrates segmented high frequency force balance (HFFB) testing with a multi-modal stochastic vibration analysis, enabling the precise assessment of wind load distribution and dynamic response. Five representative segment models are tested to quantify both mean and dynamic wind loads, a strategy rigorously validated against whole-model HFFB tests. Key findings reveal significant aerodynamic disparities among structural segments. The long-span beam, Segment 5, exhibits markedly higher and direction-dependent responses. Its mean base shear coefficient reaches 4.34 at β = 75°, which is more than twice the values of 1.74 to 2.27 for typical tower segments. Furthermore, its RMS wind force coefficient peaks at 0.65 at β = 60°, a value 2.5 to 4 times higher than those of the tower segments, all of which remained below 0.26. Furthermore, a computational model incorporating structural modes, spatial coherence, and cross-modal contributions is developed to predict wind-induced responses, validated through aeroelastic model tests. The proposed framework accurately resolves spatial wind load distribution and dynamic wind-induced response, providing a reliable and efficient tool for the wind-resistant design of multi-span UHV lattice gantries.

Through the electrowetting on dielectric effect, we attempted to control the movement of a droplet sliding on an inclined plate owing to gravity. The electrode boundary of the substrate was deflected from the in-plane gravitational direction, and the behavior of a droplet sliding on the substrate was investigated. The maximum volume that could slide along the electrode boundary was obtained theoretically from the force balance between the surface tension acting on the contact line and the gravitational force. The calculated results were in good agreement with the experimental results. For the substrate manufactured in this experiment, a maximum deflection angle of 55° was obtained for a 28 μL droplet. We created a device to sort the volume of droplets from different sliding paths depending on each volume. By installing electrode boundaries with different inclinations on the substrate, it was confirmed that the droplets actually slid in different paths and were classified in a predetermined position according to their volumes.

We consider the numerical simulation of blood flows in a patient-specific kidney including the renal artery, the renal vein, and the kidney tissue using a coupled system of unsteady Stokes-Darcy equations. The Stokes equations and the Darcy equations are implicitly coupled on the interfaces by enforcing three conditions, namely the conservation of mass, the balance of the normal force and the Beavers-Joseph-Saffman condition. To discretize the system we introduce a stabilized P1-P1-P1 finite element method for the spatial variables and an implicit backward Euler method for the temporal variable. A mathematical theory is developed to guarantee the stability and the convergence of the proposed discretization method. To efficiently solve the large, sparse and highly ill-conditioned algebraic systems, we further propose a Krylov subspace method preconditioned by a robust two-scale additive Schwarz method consisting of a mixed-dimensional coarse preconditioner with a 1D central-line preconditioner in the vascular region and a 3D preconditioner for the kidney tissue with some compatibility conditions imposed on the 1D and 3D interfaces. Some numerical experiments for a benchmark problem and a patient-specific kidney with physiologic parameters are presented to verify the accuracy, the robustness, and the effectiveness of the proposed method.

Tests were carried out in a university-type atmospheric wind tunnel on a NATO-designed Swept Wing Flow Test (SWiFT) model at incompressible Mach numbers and Reynolds numbers (Re) ranging from Re=0.2×106 to Re=2×106. The initial purpose was to compare the current results with those obtained in the National Transonic Facility (NTF) to assess the significance of Re on the physics of the flow. Following the excellent agreement in force balance data, the investigation expanded to study the leading-edge vortex (LEV) that impacts the pitch dependence on incidence and the flow unsteadiness after its liftoff from the surface, potentially leading to buffet. Oil flow visualization identified the liftoff location and its effect on pitch, while smoke visualization revealed the unsteadiness of the process. Quantitative analysis using particle image velocimetry (PIV) and hot wire anemometry exposed large periodic oscillations contributing to a turbulence level that is much larger than is known in a typical turbulent boundary layer on the verge of separation. Proper orthogonal decomposition (POD) confirmed the unsteady behavior at incidence angles exceeding vortex liftoff that raised the significance of a convective length scale and Strouhal number on this type of blended-wing–body configuration.

Stable acoustic levitation based on coaxial confocal dual-frequency focused ultrasound and vortex beams.

The universal constant π has been assigned a nonconverging value of approximately 3.145…, and this non-repeating, non-terminating decimal extends to millions—even trillions—of digits beyond the decimal point, as calculated by the most advanced computational methods. However, for thousands of years, mathematicians across different civilizations have attempted to determine the value of this fundamental constant in various ways. In geometry, angles are commonly expressed in terms of π radians, and π appears prominently in the formulas used to calculate the areas and volumes of curved geometrical figures such as circles, ellipses, spheres, cones, pyramids, and cylinders. Thus, π has become an integral part of how we measure areas and volumes. Ancient scientists, in their efforts to understand and quantify the dimensions of curved or non-linear topological objects, sensed a recurring spatial constant underlying these forms. Over time, this invariant quantity came to be known as “pi.” The pursuit of its exact value has become a continuous endeavour spanning millennia, with each generation refining its estimation using increasingly sophisticated tools and methods. In this article, it is first emphasised that, although the mathematical parameters of area and volume have traditionally been expressed through formulas involving length, breadth, and height, their more profound physical significance has not been adequately explored. This work attempts to redefine area and volume fundamentally in terms of distance or length alone, offering new mathematical formulations for the areas and volumes of basic geometric shapes such as squares, cubes, circles, spheres, and others. Another critical shortcoming of conventional mathematics lies in its neglect of the reciprocal or inverse space of the universe when evaluating the value of π. In recent research, it has been proposed that π itself represents a circle whose radius corresponds to the smallest conceivable length in the universe. Furthermore, the existence of an inverse π—always in conjugation and equilibrium with π—is posited as essential for maintaining the balance of forces in the universe. Accordingly, this article presents a novel derivation of π by simultaneously considering both the cosmos’ direct space and the reciprocal (or inverse) space.